Question

Classifique e resolva o sistema linear
2x+3y+z=11
x+y+z=6
5x+2y+3z= 18

Answer 1

ESCALONAMENTO

x+y+z= 6
2x+3y+z= 11
5x+2y+3z=18

-2 L1 + L2

-2x - 2y -2z = -12
2x + 3y + z = 11

y - z = -1

-5 L1 + L3

-5x - 5y - 5z = -30
5x + 2y + 3z = 18

-3y - 2z = -12

portanto temos

x+y+z= 6
y - z = -1
-3y - 2z = -12

3L2 + L3

3y - 3z = -3

-3y - 2z = -12

-5z = -15

z = 3

y - z = -1

y = -1 + z

y = 2

x = 6 - y - z

x = 6 - 2 - 3

x = 1

S = { 1,2,3 }